Nonlinear output feedback H∞ control for polynomial nonlinear systems

In this paper, we propose a computational scheme of solving the output feedback H_infin control problem for a class of nonlinear systems with polynomial vector field. The output feedback control design problem will be decomposed into a state feedback and an output estimation problems. Resorting to higher order Lyapunov functions, two Hamilton-Jacobian-Isaacs (HJI) inequalities are first formulated as semi-definite optimization conditions. Sum-of-squares (SOS) programming techniques are then applied to obtain computationally tractable solutions, from which a nonlinear control law will be constructed. The closed-loop system is asymptotically stabilizable by the nonlinear output feedback control and achieves good H_infin performance under the exogenous disturbances.